Now you're into trigonometry.

Basically, you have two triangles. Let's call them ABC and ABC' where A is the point described by the hinge, B is the point where the spring attaches to the box, C is the point where the spring attaches to the lid when it's open, and C' is the point where the spring attaches to the lid when it's closed. There's also a line AA' that is parallel to the ground and (obviously) passes through A.

Data points you can define are the angles CAA' and C'AA', and the ratio between the lengths AC and AC' (probably 1:1, though it seems like there might be some possibilities for it to be different).

Limitations are the maximum and minimum lengths of BC and BC'.

I've attached a GeoGebra doc that should let you play around with it. The blue point below the x-axis is free. You can move it around and see what effect it has on the angles and distances. (The point names in the doc are not the same as the point names I described above.)